Surface Area of Sphere
- $A = 4 \pi a^2$
His proof appears as Proposition $34$ in his On the Sphere and Cylinder.
He also discusses this result in his The Method:
- From this theorem, to the effect that a sphere is four times as great as the cone with a great circle of the sphere as base and height equal to the radius of the sphere, I conceived the notion that the surface of any sphere is four times as great as a great circle in it; for, judging from the fact that any circle is equal to a triangle with base equal to the circumference and height equal to the radius of the circle, I apprehended that, in like manner, a sphere is equal to a cone with base equal to the surface of the sphere and height equal to the radius.